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Scaling hypotheses, fractals

To get a first crude estimate of the frequency dependence of the modulus we put forward a simple dynamic scaling argument. It uses d in the same spirit as the exponent z in the dynamic scaling hypothesis in phase transitions according to the theory of Halperin and Hohenberg. Consider the modulus of an entropy-dominated or Brownian system which can be written from dimensional analysis as G kT/V, where V is the volume and kT the thermal energy unit. Here K is a fractal... [Pg.1010]

Mandelbrot (24) has suggested a different approach to surface irregularity by using fractal dimensions. A recent proliferation of studies has substantiated the hypothesis of self similarity for a number of natural systems ( 71-73V By this approach, surface irregularity scaling is given by the fractal dimension D, whose range is defined as 2 < D < 3 and which is related to the surface area by the proportionality... [Pg.465]

In the models of the irreversible aggregation, general concepts for the physical processes such as scaling and classes of the universality are widely used [10]. The sense of scaling (scale invariance) consists in abstracting from the details of structure and allocation of simple universal features that are the characteristic for a wide class of systems. Frequently used scaling parameters (indices) are the fractal dimensions. The hypothesis of the universality is closely connected to the hypothesis of scaling whose essence comprises... [Pg.259]

In Figure 5-3, the suscephbility /(< )/( -I-1) is reported. Therefore, from equation (5-7) and from the hypothesis that C(independent measurement of the fractal dimension from SANS experiments, D= 2.4 (Vacher, 1988), and of the spectral dimension by INS experiments, d= 1.3 0.1 (Vacher, 1989, 1990 Courtens, 1990), aUowed the determination of the scaling exponent of C(Different models have been proposed for the calculahon of C(ft>), based on the scaling properties ofthe local strain in fractals (Boukenter,... [Pg.782]


See other pages where Scaling hypotheses, fractals is mentioned: [Pg.231]    [Pg.83]    [Pg.1011]    [Pg.185]    [Pg.132]    [Pg.68]    [Pg.1009]    [Pg.139]    [Pg.84]    [Pg.1093]    [Pg.242]    [Pg.1074]   
See also in sourсe #XX -- [ Pg.185 , Pg.187 ]




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Scaling fractal

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